When the Wheatstone bridge shown in the figure is used to find the value of resistor $${R_x},$$ the galvanometer $$G$$ indicates zero current when $${R_1} = 50\,\Omega ,\,\,{R_2} = 65\,\Omega $$ and $$\,{R_3} = 100\,\Omega ,\,\,$$ If $${R_3}$$ is known with $$\, \pm 5\% \,$$ tolerance on its nominal value of $$100\,\Omega .$$ What is the range of $${R_x}$$ in Ohms?

An unbalanced $$DC$$ Wheatstone bridge is shown in the figure. At what value of $$p$$ will the magnitude of $${V_0}$$ be maximum?

A separately excited DC generator has an armature resistance of 0.1 $$\Omega$$ and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is 200 V. When this generator is operated at half the rated speed, with half the rated field current, an un-charged 1000 μF capacitor is suddenly connected across the armature terminals. Assume that the speed remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach 25 V?

A separately excited DC motor runs at 1000 rpm on no load when its armature terminals are connected to a 200 V DC source and the rated voltage is applied to the field winding. The armature resistance of this motor is 1 Ω. The no-load armature current is negligible. With the motor developing its full load torque, the armature voltage is set so that the rotor speed is 500 rpm. When the load torque is reduced to 50% of the full load value under the same armature voltage conditions, the speed rises to 520 rpm. Neglecting the rotational losses, the full load armature current (in Ampere) is _______.